D_exp_2
Matt Green
dat_full <- preprocessing(root_dir, data_dir)
dat <- subset(dat_full, subset=RT>0 & RT<25000) # loses 2 RTs that were judged to be outliers 25978 49871
dat_borderline <- dat
dat <- perSubjectTrim.fnc(dat, response='RT', subject='Subject', trim = 2.5)$data## ......
## n.removed = 204
## percent.removed = 2.797203dat$RT_log <- log(dat$RT)Info and Procedure (Method)
The main aim of this experiment was to see whether vague instructions would confer advantages over crisp alternatives when all instructions used numerals, and when there were vague and crisp versions of each of the comparison and matching strategies.
On each trial, first the referring expression that constituted the instruction for that trial was displayed (e.g., “Choose a square with about 10 dots”). Participants then pressed a key to indicate that they had read the instruction.
The instruction remained on screen, and after 1000 ms, the arrays appeared (see Figure below).
Response time was measured from the presentation of the arrays until the keypress indicating the participant’s choice. The trial would timeout after 60 seconds if there was no response.
In this experiment, no feedback was given. This was because, in the vague conditions, we did not regard any response as “correct” or “incorrect”, but instead as “expected response”; “borderline response”; and “extreme response”, and we did not want to draw participants’ attention to this distinction explicitly. Which choice the participant made was recorded for analysis.
Full table of instructions
The instructions for this experiment were similar to C_exp_2, except that we changed “fewer than” to “far fewer than”: this was because “far fewer than” can have borderline cases whereas “fewer than” cannot have borderline cases.
| Item | Quantity | Selection | Crisp | Vague |
|---|---|---|---|---|
| 06:15:24 | Small | Comparison | Choose a square with fewer than 20 dots | Choose a square with far fewer than 20 dots |
| 06:15:24 | Small | Matching | Choose a square with 6 dots | Choose a square with about 10 dots |
| 06:15:24 | Large | Comparison | Choose a square with more than 10 dots | Choose a square with far more than 10 dots |
| 06:15:24 | Large | Matching | Choose a square with 24 dots | Choose a square with about 20 dots |
| 16:25:34 | Small | Comparison | Choose a square with fewer than 30 dots | Choose a square with far fewer than 30 dots |
| 16:25:34 | Small | Matching | Choose a square with 16 dots | Choose a square with about 20 dots |
| 16:25:34 | Large | Comparison | Choose a square with more than 20 dots | Choose a square with far more than 20 dots |
| 16:25:34 | Large | Matching | Choose a square with 34 dots | Choose a square with about 30 dots |
| 26:35:44 | Small | Comparison | Choose a square with fewer than 40 dots | Choose a square with far fewer than 40 dots |
| 26:35:44 | Small | Matching | Choose a square with 26 dots | Choose a square with about 30 dots |
| 26:35:44 | Large | Comparison | Choose a square with more than 30 dots | Choose a square with far more than 30 dots |
| 26:35:44 | Large | Matching | Choose a square with 44 dots | Choose a square with about 40 dots |
| 36:45:54 | Small | Comparison | Choose a square with fewer than 50 dots | Choose a square with far fewer than 50 dots |
| 36:45:54 | Small | Matching | Choose a square with 36 dots | Choose a square with about 40 dots |
| 36:45:54 | Large | Comparison | Choose a square with more than 40 dots | Choose a square with far more than 40 dots |
| 36:45:54 | Large | Matching | Choose a square with 54 dots | Choose a square with about 50 dots |
Means plots
dat_plot <- summarySEwithin2(dat, measurevar="RT_log", withinvars=c("Vagueness", "Selection", "Item"), idvar="Subject")
Hypotheses
We formulated the following hypotheses:
- [Hypothesis 1] Crisp/Vague RT:
- Vague instructions should result in faster responses than crisp instructions.
- [Hypothesis 2] Comparison/Matching RT:
- Instructions that allow comparison should result in faster responses than instructions that necessitate matching.
- [Hypothesis 3] Vagueness effect differs between comparison and matching:
- The effects of vagueness should differ when the selection task is comparison versus when it is matching.
Results
Response times were trimmed at 25,000 ms, resulting in the loss of 2 trials that were judged to have outlier RTs. The remaining data were trimmed separately for each participant at 2.5 standard deviations below and above that participant’s mean RT, leading to the loss of 204 trials (2.8% of the remaining trials). RTs in milliseconds were log-transformed so that they better approximated a normal distribution for the purposes of analysis.
The first set of models
The first set of models considered included main effects of Vagueness and Item as well as their interaction.
dat_model <- dat
dat_model$c_Vag <- ifelse(dat_model$Vagueness=="Crisp", -0.5, 0.5)
dat_model$c_Sel <- ifelse(dat_model$Selection=="Comparison", -0.5, 0.5)
dat_model$c_Itm <- ifelse(dat_model$Item=="06:15:24", -.75, ifelse(dat_model$Item=="16:25:34", -.25, ifelse(dat_model$Item=="26:35:44", .25, .75)))
rtlmer = lmerTest::lmer(data=dat_model, RT_log ~ c_Vag * c_Sel + c_Itm + (1 + c_Vag * c_Sel + c_Itm | Subject))
pretty_coef_table(rtlmer, "rt_lmer_full_model_all_items")| term | 𝛽 | s.e. | d.f. | 𝑡 | 𝑝 | Pr(>|t|) | sig. |
|---|---|---|---|---|---|---|---|
| c_Vag | -0.0051 | 0.014 | 36.94 | -0.37 | 7.16e-01 | 0.716 | |
| c_Sel | 0.1619 | 0.026 | 36.99 | 6.24 | 2.97e-07 | <0.001 | ＊＊＊ |
| c_Itm | 0.0580 | 0.018 | 36.92 | 3.23 | 2.60e-03 | <0.01 | ＊＊ |
| c_Vag:c_Sel | 0.1324 | 0.031 | 36.87 | 4.23 | 1.49e-04 | <0.001 | ＊＊＊ |
dat_model <- subset(dat, subset=Selection=='Comparison')
dat_model$c_Vag <- ifelse(dat_model$Vagueness=="Crisp", -0.5, 0.5)
dat_model$c_Itm <- ifelse(dat_model$Item=="06:15:24", -.75, ifelse(dat_model$Item=="16:25:34", -.25, ifelse(dat_model$Item=="26:35:44", .25, .75)))
comp_lmer <- lmerTest::lmer(data=dat_model, RT_log ~ c_Vag + c_Itm + (1 + c_Vag + c_Itm | Subject))
pretty_coef_table(comp_lmer, "rt_lmer_for_comparison_all_items")| term | 𝛽 | s.e. | d.f. | 𝑡 | 𝑝 | Pr(>|t|) | sig. |
|---|---|---|---|---|---|---|---|
| c_Vag | -0.071 | 0.020 | 36.99 | -3.52 | 1.15e-03 | <0.01 | ＊＊ |
| c_Itm | 0.090 | 0.020 | 37.02 | 4.61 | 4.68e-05 | <0.001 | ＊＊＊ |
dat_model <- subset(dat, subset=Selection=='Matching')
dat_model$c_Vag <- ifelse(dat_model$Vagueness=="Crisp", -0.5, 0.5)
dat_model$c_Itm <- ifelse(dat_model$Item=="06:15:24", -.75, ifelse(dat_model$Item=="16:25:34", -.25, ifelse(dat_model$Item=="26:35:44", .25, .75)))
match_lmer <- lmerTest::lmer(data=dat_model, RT_log ~ c_Vag + c_Itm + (1 + c_Vag + c_Itm | Subject))
pretty_coef_table(match_lmer, "rt_lmer_for_matching_all_items")| term | 𝛽 | s.e. | d.f. | 𝑡 | 𝑝 | Pr(>|t|) | sig. |
|---|---|---|---|---|---|---|---|
| c_Vag | 0.062 | 0.021 | 36.32 | 2.91 | 6.14e-03 | <0.01 | ＊＊ |
| c_Itm | 0.025 | 0.022 | 36.62 | 1.12 | 2.71e-01 | 0.271 |
Considering the first set of models with Vagueness and Item as main effects and the Vagueness:Item interaction in the same model:
- [Hypothesis 1] Crisp/Vague RT:
- Vague instructions should result in faster responses than crisp instructions : Vague instructions resulted in faster responses than crisp instructions but the difference was not significant (p=0.716).
- [Hypothesis 2] Comparison/Matching RT:
- Instructions that allow comparison should result in faster responses than instructions that necessitate matching : comparison instructions resulted in faster responses than matching instructions, and the difference was significant (p<0.001).
- [Hypothesis 3] Vagueness effect differs between comparison and matching
- The effects of vagueness should differ when the selection task is comparison versus when it is matching : Vagueness exerted effects in different directions for the two selection tasks (p<0.001). Separate analyses at each level of selection provided evidence that vague instructions resulted in faster responses than crisp instructions for the comparison condition (p<0.01); and slower responses than crisp instructions in the matching condition (p<0.01).